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PyMC tries to make standard things easy, but keep unusual things possible. Its
openness, combined with Python’s flexibility, invite extensions from using new
step methods to exotic stochastic processes (see the Gaussian process module).
This chapter briefly reviews the ways PyMC is designed to be extended.

The simplest way to create a Stochastic object with a nonstandard
distribution is to use the medium or long decorator syntax. See Chapter
Building models. If you want to create many stochastics with the same
nonstandard distribution, the decorator syntax can become cumbersome. An actual
subclass of Stochastic can be created using the class factory
stochastic_from_dist. This function takes the following arguments:

The name of the new class,

A logp function,

A random function,

The NumPy datatype of the new class (for continuous distributions, this
should be float; for discrete distributions, int; for variables
valued as non-numerical objects, object),

The StepMethod class is meant to be subclassed. There are an enormous number of MCMC step methods in the literature, whereas PyMC provides only about half a dozen. Most user-defined step methods will be either Metropolis-Hastings or Gibbs step methods, and these should subclass Metropolis or Gibbs respectively. More unusual step methods should subclass StepMethod directly.

The stochastic variable cutoff cannot be smaller than the largest element
of \(D\), otherwise \(D\)‘s density would be zero. The standard
Metropolis step method can handle this case without problems; it will
propose illegal values occasionally, but these will be rejected.

Suppose we want to handle cutoff with a smarter step method that doesn’t
propose illegal values. Specifically, we want to use the nonsymmetric proposal
distribution:

The propose method sets the step method’s stochastic’s value to a new
value, drawn from a truncated normal distribution. The precision of this
distribution is computed from two factors: self.proposal_sd, which can be
set with an input argument to Metropolis, and self.adaptive_scale_factor.
Metropolis step methods’ default tuning behavior is to reduce
adaptive_scale_factor if the acceptance rate is too low, and to increase
adaptive_scale_factor if it is too high. By incorporating
adaptive_scale_factor into the proposal standard deviation, we avoid having
to write our own tuning infrastructure. If we don’t want the proposal to tune,
we don’t have to use adaptive_scale_factor.

The hastings_factor method adjusts for the asymmetric proposal distribution
[Gelman2004]. It computes the log of the quotient of the ‘backward’ density
and the ‘forward’ density. For symmetric proposal distributions, this quotient
is 1, so its log is zero.

Having created our custom step method, we need to tell MCMC instances to use it
to handle the variable cutoff. This is done in custom_step.py with
the following line:

M.use_step_method(TruncatedMetropolis,cutoff,D.value.max(),np.inf)

This call causes \(M\) to pass the arguments cutoff, D.value.max(),
and np.inf to a TruncatedMetropolis object’s __init__ method, and
use the object to handle cutoff.

Its often convenient to get a handle to a custom step method instance directly
for debugging purposes. M.step_method_dict[cutoff] returns a list of all
the step methods \(M\) will use to handle cutoff:

Tunes the jumping strategy based on performance so far. A default method is
available that increases self.adaptive_scale_factor (see below) when
acceptance rate is high, and decreases it when acceptance rate is low. This
method should return True if additional tuning will be required later,

and False otherwise.

competence(s):

A class method that examines stochastic variable \(s\) and returns a

value from 0 to 3 expressing the step method’s ability to handle the
variable. This method is used by MCMC instances when automatically
assigning step methods. Conventions are:

0

I cannot safely handle this variable.

1

I can handle the variable about as well as the standard Metropolis step method.

2

I can do better than Metropolis.

3

I am the best step method you are likely to find for this variable in most cases.

For example, if you write a step method that can handle
MyStochasticSubclass well, the competence method might look like this:

Note that PyMC will not even attempt to assign a step method automatically
if its __init__ method cannot be called with a single stochastic
instance, that is MyStepMethod(x) is a legal call. The list of step
methods that PyMC will consider assigning automatically is called
pymc.StepMethodRegistry.

current_state():

This method is easiest to explain by showing the code:

state={}forsinself._state:state[s]=getattr(self,s)returnstate

self._state should be a list containing the names of the attributes
needed to reproduce the current jumping strategy. If an MCMC object
writes its state out to a database, these attributes will be preserved. If
an MCMC object restores its state from the database later, the
corresponding step method will have these attributes set to their saved
values.

Step methods should also maintain the following attributes:

_id:

A string that can identify each step method uniquely (usually something

like <class_name>_<stochastic_name>).

adaptive_scale_factor:

An ‘adaptive scale factor’. This attribute is only needed if the default
tune() method is used.

_tuning_info:

A list of strings giving the names of any tuning parameters. For

Metropolis instances, this would be adaptive_scale_factor. This
list is used to keep traces of tuning parameters in order to verify
‘diminishing tuning’ [Roberts2007].

All step methods have a property called loglike, which returns the sum of
the log-probabilities of the union of the extended children of
self.stochastics. This quantity is one term in the log of the Metropolis-
Hastings acceptance ratio. The logp_plus_loglike property gives the sum of
that and the log-probabilities of self.stochastics.

Sets the values of all self.stochastics to new, proposed values. This
method may use the adaptive_scale_factor attribute to take advantage of
the standard tuning scheme.

Metropolis-Hastings step methods may also override the tune and competence methods.

Metropolis-Hastings step methods with asymmetric jumping distributions may
implement a method called hastings_factor(), which returns the log of the
ratio of the ‘reverse’ and ‘forward’ proposal probabilities. Note that no
accept() method is needed or used.

By convention, Metropolis-Hastings step methods use attributes called
accepted and rejected to log their performance.

Gibbs step methods handle conjugate submodels. These models usually have two
components: the ‘parent’ and the ‘children’. For example, a gamma-distributed
variable serving as the precision of several normally-distributed variables is
a conjugate submodel; the gamma variable is the parent and the normal variables
are the children.

This section describes PyMC’s current scheme for Gibbs step methods, several of
which are in a semi-working state in the sandbox directory. It is meant to be
as generic as possible to minimize code duplication, but it is admittedly
complicated. Feel free to subclass StepMethod directly when writing Gibbs
step methods if you prefer.

Gibbs step methods that subclass PyMC’s Gibbs should define the following
class attributes:

child_class:

The class of the children in the submodels the step method can handle.

parent_class:

The class of the parent.

parent_label:

The label the children would apply to the parent in a conjugate submodel.

In the gamma-normal example, this would be tau.

linear_OK:

A flag indicating whether the children can use linear combinations

involving the parent as their actual parent without destroying the
conjugacy.

A subclass of Gibbs that defines these attributes only needs to implement a
propose() method, which will be called by Gibbs.step(). The resulting
step method will be able to handle both conjugate and ‘non-conjugate’ cases.
The conjugate case corresponds to an actual conjugate submodel. In the
non-conjugate case all the children are of the required class, but the parent
is not. In this case the parent’s value is proposed from the likelihood and
accepted based on its prior. The acceptance rate in the non-conjugate case will
be less than one.

The inherited class method Gibbs.competence will determine the new step
method’s ability to handle a variable \(x\) by checking whether:

all \(x\)‘s children are of class child_class, and either apply
parent_label to \(x\) directly or (if linear_OK=True) to a
LinearCombination object (chapter Building models), one of
whose parents contains \(x\).

\(x\) is of class parent_class

If both conditions are met, pymc.conjugate_Gibbs_competence will be
returned. If only the first is met, pymc.nonconjugate_Gibbs_competence will
be returned.

PyMC provides a convenient platform for non-MCMC fitting algorithms in addition
to MCMC. All fitting algorithms should be implemented by subclasses of
Model. There are virtually no restrictions on fitting algorithms, but many
of Model’s behaviors may be useful. See Chapter Fitting Models.

Unless there is a good reason to do otherwise, Monte Carlo fitting algorithms
should be implemented by subclasses of Sampler to take advantage of the
interactive sampling feature and database backends. Subclasses using the
standard sample() and isample() methods must define one of two methods:

draw():

If it is possible to generate an independent sample from the posterior at

every iteration, the draw method should do so. The default _loop
method can be used in this case.

_loop():

If it is not possible to implement a draw() method, but you want to

take advantage of the interactive sampling option, you should override
_loop(). This method is responsible for generating the posterior
samples and calling tally() when it is appropriate to save the model’s
state. In addition, _loop should monitor the sampler’s status
attribute at every iteration and respond appropriately. The possible values
of status are:

'ready':

Ready to sample.

'running':

Sampling should continue as normal.

'halt':

Sampling should halt as soon as possible. _loop should call the
halt() method and return control. _loop can set the status to
'halt' itself if appropriate (eg the database is full or a
KeyboardInterrupt has been caught).

'paused':

Sampling should pause as soon as possible. _loop should return, but
should be able to pick up where it left off next time it’s called.

Samplers may alternatively want to override the default sample() method. In
that case, they should call the tally() method whenever it is appropriate
to save the current model state. Like custom _loop() methods, custom
sample() methods should handle KeyboardInterrupts and call the
halt() method when sampling terminates to finalize the traces.

If you’re going to implement a new step method, fitting algorithm or unusual (non-numeric-valued) Stochastic subclass, you should understand the issues related to in-place updates of Stochastic objects’ values. Fitting methods should never update variables’ values in-place for two reasons:

In algorithms that involve accepting and rejecting proposals, the ‘pre-proposal’ value needs to be preserved uncorrupted. It would be possible to make a copy of the pre-proposal value and then allow in-place updates, but in PyMC we have chosen to store the pre-proposal value as Stochastic.last_value and require proposed values to be new objects. In-place updates would corrupt Stochastic.last_value, and this would cause problems.

LazyFunction’s caching scheme checks variables’ current values against its internal cache by reference. That means if you update a variable’s value in-place, it or its child may miss the update and incorrectly skip recomputing its value or log-probability.

However, a Stochastic object’s value can make in-place updates to itself if the updates don’t change its identity. For example, the Stochastic subclass gp.GP is valued as a gp.Realization object. GP realizations represent random functions, which are infinite-dimensional stochastic processes, as literally as possible. The strategy they employ is to ‘self-discover’ on demand: when they are evaluated, they generate the required value conditional on previous evaluations and then make an internal note of it. This is an in-place update, but it is done to provide the same behavior as a single random function whose value everywhere has been determined since it was created.